Al can paint a room in a hours working alone. Bill can paint a room in b hours working alone. Working alone, Bill takes tow more hours to paint a room than Al. Working together, they can paint a room in 8 hours. Write down a system of two equations involving the variables a and b that can be used to find a and b. Solve the system.

Question

Al can paint a room in a hours working alone. Bill can paint a room in b hours working alone. Working alone, Bill takes tow more hours to paint a room than Al. Working together, they can paint a room in 8 hours. Write down a system of two equations involving the variables a and b that can be used to find a and b. Solve the system.

b=a+2
a+b=8
substitute and solve

Answer 1

To write down a system of two equations involving the variables a and b, we can use the given information:

1. From the statement "Bill takes two more hours to paint a room than Al," we can write the equation: b = a + 2.

2. From the statement "Working together, they can paint a room in 8 hours," we can write the equation: a + b = 8.

Now, to solve the system, we can substitute the first equation into the second equation:

a + (a + 2) = 8.

Simplifying this equation, we get:

2a + 2 = 8.

Subtracting 2 from both sides of the equation, we have:

2a = 6.

Dividing both sides of the equation by 2, we get:

a = 3.

Now, we can substitute the value of a into the first equation to find the value of b:

b = 3 + 2 = 5.

Therefore, the solutions to the system of equations are a = 3 and b = 5.